Study of Magnetohydrodynamic and Thermal Characteristics of Axisymmetric Stagnation Point Flow with Viscous Dissipation over a Shrinking Surface

A study of magnetohydrodynamics (MHD) axisymmetric stagnation point flow with viscous dissipation and heat transfer in an electrically conducting laminar steady viscous incompressible fluid over a heated axisymmetric shrinking surface is presented. The governing partial differential equations (PDEs) are reduced to non linear ordinary differential equations (ODEs) in dimensionless form using suitable similarity transformations. The transformed ODEs are solved numerically by an algorithm based on finite difference approximations. The results show profound effects of the shrinking and the transverse magnetic field on the hydrodynamic and thermal characteristics of the flow. In some features like boundary layer thickness these phenomena are contending with each other while in others like viscous dissipation, these are supportive to each other. Reversal of heat transfer direction from solid-to-fluid to fluid-to-solid starts at smaller values of the Eckert number depending on the shrinking rate and the strength of the magnetic field. Therefore, in the presence of either or both of the shrinking in the heated surface and the magnetic field in the flow, viscous dissipation cannot be brutally neglected. In view of the shrinking rate and the strength of the applied magnetic field, careful assessment must be made in order to decide whether viscous dissipation is to be neglected or not.